Structural Engineering and Mechanics

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Energy equivalent lumped damage model for reinforced concrete structures

  • Neto, Renerio Pereira (Laboratory of Mathematical Modelling in Civil Engineering, Post-Graduate Programme in Civil Engineering, Federal University of Sergipe) ;
  • Teles, Daniel V.C. (Laboratory of Mathematical Modelling in Civil Engineering, Post-Graduate Programme in Civil Engineering, Federal University of Sergipe) ;
  • Vieira, Camila S. (Laboratory of Mathematical Modelling in Civil Engineering, Post-Graduate Programme in Civil Engineering, Federal University of Sergipe) ;
  • Amorim, David L.N.F. (Laboratory of Mathematical Modelling in Civil Engineering, Post-Graduate Programme in Civil Engineering, Federal University of Sergipe)
  • Received : 2021.09.22
  • Accepted : 2022.09.18
  • Published : 2022.10.25
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Abstract

Lumped damage mechanics (LDM) is a recent nonlinear theory with several applications to civil engineering structures, such as reinforced concrete and steel buildings. LDM apply key concepts of classic fracture and damage mechanics on plastic hinges. Therefore, the lumped damage models are quite successful in reproduce actual structural behaviour using concepts well-known by engineers in practice, such as ultimate moment and first cracking moment of reinforced concrete elements. So far, lumped damage models are based in the strain energy equivalence hypothesis, which is one of the fictitious states where the intact material behaviour depends on a damage variable. However, there are other possibilities, such as the energy equivalence hypothesis. Such possibilities should be explored, in order to pursue unique advantages as well as extend the LDM framework. Therewith, a lumped damage model based on the energy equivalence hypothesis is proposed in this paper. The proposed model was idealised for reinforced concrete structures, where a damage variable accounts for concrete cracking and the plastic rotation represents reinforcement yielding. The obtained results show that the proposed model is quite accurate compared to experimental responses.

Keywords

Acknowledgement

The second author acknowledges CAPES (Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior) for his M.Sc. scholarship.

References

  1. Abbas, S., Soliman, A.M. and Nehdi, M.L. (2014), "Mechanical performance of reinforced concrete and steel fiber-reinforced concrete precast tunnel lining segments: A case study", ACI Mater. J., 111(5), 501-510. https://doi.org/10.14359/51687101.
  2. Alva, G.M.S. and El Debs, A.L.H.C. (2010), "Application of lumped dissipation model in nonlinear analysis of reinforced concrete structures", Eng. Struct., 32(4), 974-981. https://doi.org/10.1016/j.engstruct.2009.12.024.
  3. Amorim, D.L.N.F., Proenca, S.P.B. and Florez-Lopez, J. (2013), "A model of fracture in reinforced concrete arches based on lumped damage mechanics", Int. J. Solid. Struct., 50(24), 4070-4079. https://doi.org/10.1016/j.ijsolstr.2013.08.012.
  4. Amorim, D.L.N.F., Proenca, S.P.B. and Florez-Lopez, J. (2014), "Simplified modeling of cracking in concrete: Application in tunnel linings", Eng. Struct., 70, 23-35. https://doi.org/10.1016/j.engstruct.2014.03.031.
  5. Araujo, F. and Proenca, S.P.B. (2008), "Application of a lumped dissipation model to reinforced concrete structures with the consideration of residual strains and cycles of hysteresis", J. Mech. Mater. Struct., 3(5), 1011-1031. https://doi.org/10.2140/jomms.2008.3.1011.
  6. Bai, Y., Guan, S. and Florez-Lopez, J. (2017), "Development of a damage model for assessing fracture failure of steel beam-to-column connections subjected to extremely low-cycle fatigue", Eng. Fail. Anal., 82, 823-834. https://doi.org/10.1016/j.engfailanal.2017.07.032.
  7. Bai, Y., Kurata, M., Florez-Lopez, J. and Nakashima, M. (2016), "Macromodeling of crack damage in steel beams subjected to nonstationary low cycle fatigue", J. Struct. Eng., 142, 60-76. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001536
  8. Barrios, S.K.M. and Florez-Lopez, J. (2020), "Numerical quantification of damage reduction in frames retrofitted with FRP bands as bracing elements", Eng. Struct., 223, 111178. https://doi.org/10.1016/j.engstruct.2020.111178.
  9. Basaran, C., Tang, H. and Nie, S. (2002), "Experimental damage mechanics of microelectronics solder joints under fatigue loading", ASME 2002 International Mechanical Engineering Congress and Exposition, 36401, 229-236.
  10. Bazan, J.A.V., Beck, A.T. and Florez-Lopez, J. (2019), "Random fatigue of plane frames via lumped damage mechanics", Eng. Struct., 182, 301-315. https://doi.org/10.1016/j.engstruct.2018.12.008.
  11. Borino, G., Failla, B. and Parrinello, F. (2003), "A symmetric nonlocal damage theory", Int. J. Solid. Struct., 40(13-14), 3621-3645. https://doi.org/10.1016/S0020-7683(03)00144-6.
  12. Brito, T.I.J., Santos, D.M., Santos, F.A.S., Cunha, R.N. and Amorim, D.L.N.F. (2020), "On the lumped damage modelling of reinforced concrete beams and arches", Frat. ed Integrita Strutt., 14(54), 1-20. https://doi.org/10.3221/IGF-ESIS.54.01.
  13. Caratelli, A., Meda, A., Rinaldi, Z. and Romualdi, P. (2011), "Structural behaviour of precast tunnel segments in fiber reinforced concrete", Tunn. Undergr. Sp. Tech., 26(2), 284-291. https://doi.org/10.1016/j.tust.2010.10.003.
  14. Cervera, M., Oliver, J. and Faria, R. (1995), "Seismic evaluation of concrete dams via continuum damage models", Earthq. Eng. Struct. Dyn., 24(9), 1225-1245. https://doi.org/10.1002/eqe.4290240905.
  15. Cipollina, A., Lopez-Inojosa, A. and Florez-Lopez, J. (1995), "A simplified damage mechanics approach to nonlinear analysis of frames", Comput. Struct., 54(6), 1113-1126. https://doi.org/10.1016/0045-7949(94)00394-I.
  16. Comi, C. and Perego, U. (2001), "Fracture energy bi-dissipative damage model for concrete", Int. J. Solid. Struct., 38(36-37), 6427-6454. https://doi.org/10.1016/S0020-7683(01)00066-X.
  17. Faleiro, J., Oller, S. and Barbat, A.H. (2010), "Plastic-damage analysis of reinforced concrete frames", Eng. Comput., 27(1), 57-83. https://doi.org/10.1108/02644401011008522.
  18. Florez-Lopez, J. (1993), "Modelos de dano concentrado para la simulacion del colapso de porticos planos", Rev. Int. Met. Num. Calc. Dis. Ing., 9, 143-159.
  19. Florez-Lopez, J., Marante, M.E. and Picon, R. (2015), "Fracture and damage mechanics for structural engineering of frames: State-of-the-art industrial applications", IGI Global, Hershey, PA, USA.
  20. Guerrero, N., Marante, M.E., Picon, R. and Florez-Lopez, J. (2009), "Analysis of Steel hollow structural beams subjected to biaxial bending by lumped damage mechanics", Rev. Int. Met. Num. Calc. Dis. Ing., 25(1), 3-27.
  21. Kachanov, L. (1958), "On the creep fracture time", Izv. Akad. Nauk. USSR Otd. Tech., 8, 26-31.
  22. Kamal, M.A., Farid, A.F. and Rashed, Y.F. (2016), "Explicit boundary element modeling of nonlocal damage with Eshelby theory", Eng. Anal. Bound. Elem., 131, 64-75. https://doi.org/10.1016/j.enganabound.2021.06.014.
  23. Lemaitre, J. and Chaboche, J.L. (1985), Mecaniques des Materiaux Solides, Dunod, Paris, France.
  24. Liu, Y.B. and Liu, J.B. (2004), "A damage beam element model for nonlinear analysis of reinforced concrete member", Earthq. Eng. Eng. Vib., 24(2), 95-100.
  25. Luccioni, B. and Oller, S. (2003), "A directional damage model", Comput. Meth. Appl. Mech. Eng., 192(9-10), 1119-1145. https://doi.org/10.1016/S0045-7825(02)00577-7.
  26. Mazars, J. (1986), "A description of micro- and macro-scale damage of concrete structures", Eng. Fract. Mech., 25(5-6), 729-737. https://doi.org/10.1016/0013-7944(86)90036-6.
  27. Mazars, J. and Grange, S. (2017), "Simplified strategies based on damage mechanics for concrete under dynamic loading", Phil. Trans. R. Soc. A, 375(2085), 20160170. https://doi.org/10.1098/rsta.2016.0170.
  28. Molladavoodi, H. and Mortazavi, A. (2011), "A damage-based numerical analysis of brittle rocks failure mechanism", Finite Elem. Anal. Des., 47(9), 991-1003. https://doi.org/10.1016/j.finel.2011.03.015.
  29. Perdomo, M.E., Picon, R., Marante, M.E., Hild, F., Roux, S. and Florez-Lopez, J. (2013), "Experimental analysis and mathematical modeling of fracture in RC elements with any aspect ratio", Eng. Struct., 46, 407-416. https://doi.org/10.1016/j.engstruct.2012.07.005.
  30. Perdomo, M.E., Ramirez, A. and Florez-Lopez, J. (1999), "Simulation of damage in RC frames with variable axial force", Earthq. Eng. Struct. D., 28(3), 311-328. https://doi.org/10.1002/(SICI)1096-9845(199903)28:3<311::AID-EQE819>3.0.CO;2-D.
  31. Rabotnov, Y. (1968), "Creep rupture", Proceedings of the Twelfth International Congress of Applied Mechanics, Stanford, USA.
  32. Rajasankar, J., Iyer, N.R. and Prasad, A.P. (2009), "Modelling inelastic hinges using CDM for nonlinear analysis of reinforced concrete frame structures", Comput. Concrete, 6(4), 319-341. http://doi.org/10.12989/cac.2009.6.4.319.
  33. Teles, D.V.C., Oliveira, M.C. and Amorim, D.L.N.F. (2020), "A simplified lumped damage model for reinforced concrete beams under impact loads", Eng. Struct., 205, 110070. https://doi.org/10.1016/j.engstruct.2019.110070.
  34. Toi, Y. and Hasegawa, K.H. (2011), "Element-size independent, elasto-plastic damage analysis of framed structures using the adaptively shifted integration technique", Comput. Struct., 89(23-24), 2162-2168. https://doi.org/10.1016/j.compstruc.2011.09.002.
  35. Voyiadjis, G.Z. and Kattan, P.I. (2009), "A comparative study of damage variables in continuum damage mechanics", Int. J. Damage Mech., 18(4), 315-340. https://doi.org/10.1177/1056789508097546.
  36. Voyiadjis, G.Z. and Kattan, P.I. (2019), "Fundamental aspects for characterization in continuum damage mechanics", Int. J. Damage Mech., 28(2), 200-218. https://doi.org/10.1177/1056789517752524.
  37. Voyiadjis, G.Z., Shojaei, A., Li, G. and Kattan, P. (2012), "Continuum damage-healing mechanics with introduction to new healing variables", Int. J. Damage Mech., 21(3), 391-414. https://doi.org/10.1177/1056789510397069.
  38. Wu, J.Y. and Cervera, M. (2018), "A novel positive/negative projection in energy norm for the damage modeling of quasibrittle solids", Int. J. Solid. Struct., 139, 250-269. https://doi.org/10.1016/j.ijsolstr.2018.02.004.
  39. Yang, T.S. and Wang, J.L. (2010), "Damage analysis of threedimensional frame structure suffering from impact", J. Vib. Shock, 29(12), 177-180.